Probabilistic Stability Analysis of a Three-Dimensional Rock Slope Characterized by the Hoek-Brown Failure Criterion

The probabilistic stability analysis of a three-dimensional rock slope is studied in this paper. The deterministic computation of the critical slope height is based on the kinematic approach of limit analysis, for which the generalized Hoek-Brown failure criterion is adopted to characterize the failure of rock masses. Sparse polynomial chaos expansion is taken to perform the probabilistic analysis using a response surface method. The uncertainties considered involve the Hoek-Brown parameters (mi, GSI, σc, and Di), slope geometry parameters (β, H, and B/H), and rock mass unit weight (γ). The influences of the uncertainty level, correlation relationships between the Hoek-Brown parameters, and distribution types are discussed. Finally, a reliability-based design chart is provided to evaluate the safety factor of a slope required for a target failure probability.